Stellar systems of the trapezium type

Stellar Systems of the Trapezium Type STEWART SHARPLESS* U.S. Naval Observatory, Washington, D.C., U.S.A. A TRAPEZIUMsystem, as defined b y AMBARTSUMIAN(1954, 1955, 1958), is a multiple star whose separations are roughly of the same order of magnitude. The Trapezium of Orion, 81 Orionis, is the prototype in which the separations of the three brightest secondary components are approximately 9, 13 and 21 sec of arc, respectively. A trapezium system differs, therefore, from the classical multiple star, such as • Lyrae, in which the distribution of separations is hierarchic and whose geometric configuration is stable indefinitely. A classical multiple star can, owing to projection effects, appear as a trapezium system. Thus, if the • Lyrae system were viewed "end-on" it would resemble ~1 Orionis in its configuration. The question arises, then, as to whether all trapezium systems can be explained in this way. In a rather elaborate statistical analysis AMBARTSUMIA:N (1954) showed that all trapezium systems having spectral types later than B9 can be accounted for on the basis of the assumption that they are classical multiple stars which appear as trapezium systems as a result of projection effects only. On the other hand, the O- and early B-type systems of the trapezium type occur in numbers considerably greater than what would be expected from projection effects alone. Ambartsumian concluded that there exist among the early type stars multiple systems whose linear separations are indeed all of the same order of magnitude. Further, he pointed out that such a configuration of stars must be dynamically unstable and that it can be expected to disintegrate in a time less than a million years. It was shown by SHARPLESS (1954) that trapezium systems are particularly frequent among the O-type stars connected with emission nebulae. An example, shown in Fig. l, is BD + 22 ° 3782 (spectral type 07) which is located in the nebula NGC 6823 and is part of the I Vulpeculae association. Approximately 15 components are visible within a radius of less than 20 sec of arc. It was suggested b y Sharpless that some apparently single O-type stars m a y be trapezium systems in an earlier stage of development and unresolved. The spectrum of such a system would generally not appear to be composite. I t is not uncommon for a trapezium system to be surrounded b y a sparse cluster of somewhat fainter stars. The Trapezium of Orion lies in the center of a faint cluster (BAADE and iV[I~XOWS~I, 1937) having a diameter of about 10 min of arc, while BD +22°3782 is surrounded b y a similar cluster of about 5 min diameter. A trapezium system m a y also be a member of a larger cluster containing other Oand m-type stars or of an association of early-type stars. In Orion we observe the following hierarchy: the Trapezium, the Trapezium cluster, and the "Sword" of * Now a t University of Rochester, Rochester, New York, U.S.A. 127

128

Stellar Systems of the Trapezium Type

Orion which, in turn, constitutes the nuclear cluster of the Orion association. These subsystems differ in size, from one to the next, b y a factor of about 10, and it has been shown by SHARPLESS (1962) that they also differ considerably in age, the smallest being the youngest. This result is consonant with the idea that the various subsystems in an association are expanding since, under this circumstance, the size of a subsystem will be proportional to its age.

•

•

0

•

•

• I

30"

•

•

I

•

O.

• •

•

FIG. 1. Field of B D ~ 22 ° 3782 drawn from photograph (103a-O emulsion) taken with 60-in. telescope at Mount Wilson Observatory. The scale is indicated at the lower left.

The dynamical instability and consequent rapid dissolution of trapezium systems offers the possibility of obtaining kinematic ages for these objects under the reasonable assumption that the dissolution began at approximately the same time that the stars themselves were formed. I t is thus possible to construct a kinematic time scale for stars of the earliest spectral types which can be compared with the time scale derived from evolutionary theories. Fortunately, micrometric observations of a number of trapezium systems were made b y W. Struve in the 1830's which are known to be of very high accuracy. The separations measured b y Struve can be

STEWART SHAI~LESS

129

combined with a modern series of photographic measures to determine the relative motions of components of these systems, hence their kinematic ages. The system having the best history of astrometric observations, both visual and photographic, is 81 Orionis. On the basis of the visual data only, PARENAGO (1953) determined the kinematic age of the Trapezium to be t~n < 104 years. This has been confirmed by FRANZ (unpublished) who, on the basis of both visual and photographic data, has obtained a preliminary value of tkin = 1"0 × 104 years with a mean error of about 15 per cent. This corresponds to a relative transverse velocity of expansion of about 7 km/sec. The range of radial velocity among the four components is about 9 km/sec. I

f

I

/

vo 3

7 -

8--

9

I -0.4

T -0.3

I -0.2

I -O.I

0.0

(B-V) o

FIG. 2. C o l o r - m a g n i t u d e d i a g r a m f o r t h e f o u r b r i g h t e s t c o m p o n e n t s of

~10rionis.

I n Fig. 2 is shown the color-magnitude diagram for the four bright members of the Trapezium based on observations made by SHARPLESS (1952) combined with more recent observations b y JOHNSON and Bo~G~_A~ (1963). The curve represents the lower envelope of the color-magnitude diagram of stars in the Sword region of Orion, i.e. the unevolved main sequence. There appears to be a marked departure from the unevolved main sequence near M~ = --4.5. The time required for gravitational contraction to bring a star to this point on the main sequence is estimated to be 1.6 × 104 years on the basis of classical contraction theory (SANDAGE, 1958). This can be compared with the kinematic age discussed earlier. Conclusions drawn on the basis of only one system must be regarded as highly tentative. However, it can be noted t h a t a kinematic age obtained by the method described here represents an upper limit since the method ignores the possible effect

130

Stellar Systemsof the Trapezium Type

of decelerations and assumes t h a t the stars initially occupied zero volume. On the other hand, the evolutionary age determined from contraction theory represents a lower limit in the sense that it ignores the possibility of thermonuclear reactions taking place during the contraction process. We might, therefore, in general expect to find observed values of tkl n which are greater than the corresponding values of tg.c" as obtained from Sandage's formula. However, in the case of 01 Orionis, just the opposite is true, i.e. tg.c. > t~in. As pointed out by Sandage, one way in which a value of tg.c"can be reduced is through the assumption t h a t fragmentation has taken place during the contraction process. But fragmentation might well be the process responsible for the multiplicity of these objects. We conclude, therefore, t h a t a hypothesis of the formation of trapezium systems through condensation from the interstellar medium and subsequent fragmentation is not contradicted by the data in the case of 0 a Orionis. Quite different ideas on the formation of these systems have been expressed by AMBARTSUM~ (1955). From the fact t h a t the members of the Trapezium are rapidly moving away from one another he concluded t h a t these systems have positive total energy, i.e. the total kinetic energy is greater than the absolute value of the gravitational potential energy of the system, regarding the stars now as mass points. To account for this, he hypothesized a "protostar" of extremely high density which divides by some unknown mechanism to form a rapidly expanding trapezium system. This differs from the classical concept of a cluster with negative total energy which ejects individual stars from time to time while the main body of the cluster contracts. Ambartsumian's hypothesis suffers from the fact t h a t such protostars are not detected, but on the other hand it is difficult to reconcile positive total energy of these systems with the hypothesis of condensation from the interstellar medium. There are two important observations which bear on the question of whether these systems have positive or negative total energy. The first of these is t h a t we observe, on the average, about one trapezium system in each O-association. Since the maximum ages of the trapezium systems are apparently much less than the ages of the associations in which they are found, we must conclude t h a t the formation of trapezium systems in an association is a recurrent phenomenon. I f we estimate t h a t the average age of an association is 5 × l0 s years and the average age of a trapezium is of the order o f 105 years, at most, then about 50 such systems have been formed on the average in each association. I f each were to produce four stars in the mass range corresponding to spectral types 0 to B5, then at least 200 such stars will have been formed in each association as a result of the dissolution of trapezium systems. I t appears, therefore, t h a t most of the more massive stars in an association m a y have found their origin in this way. This being the case, it is not unreasonable to trace the origin of the expanding motions observed in associations to the dynamical instability and consequent dissolution of these systems. The second fact t h a t bears on the question of whether trapezium systems have positive or negative total energy is BLAAUW'S(1961) discovery that almost all massive stars in an O-association are binary stars. I t appears, therefore, t h a t the dynamical instability of trapezium systems must result not in the ejection of single stars, but in the formation of stable binaries. With this in mind, it is not necessary to postulate positive total energy for these systems since the mechanism responsible for the formation of stable binaries has the effect of introducing a source of negative

STEWART SHARPLESS

131

energy. We therefore have at an early stage in the history of a trapezium system a compact group of stars which has recently condensed from the interstellar medium and which is dynamically unstable owing to close encounters among member stars. At a later stage we have, according to the evidence presented here, a number of stable binaries moving outward from their common point of origin. Let us assume, as a reasonable model for 01 0rionis, the following: n

~ 10 ~

10o

Vexp ~ 10 km/sec where n is the total number of stars in the system, ~ is their average mass, and Vexp TABLE 1 RELATI01~" BETWEEN I~ADIUS AND TOTAL EI~EI~GY IN A ~1 ORIONIS MODEL

R

~

ET

5000 A U 1500 500 150

50 A U 36 19 8

~-0.10 × 1047 erg --0.25 × 1047 - - 1 . 3 6 × 104~

--4.60 × 1047

is the final expansion velocity of the system. I t is possible to equate the expressions for the original and final total energy of the system. For various values of R, the original radius of the system, we can solve for ~, the average separation of the resulting binaries. These results are shown in Table 1 for four assumed values of R. I t is seen t h a t for an initial radius in the range covered by the last three entries of the table the mean separations of the resulting binaries are quite reasonable and the total energy of the system is negative. We can conclude t h a t the original dimensions of this system were probably of the order of 102-10 a AU. The author is continuing his photometric and spectroscopic study of the components of trapezium systems in order further to investigate their H E diagrams and color-magnitude diagrams. Astrometric data concerning a number of these systems are being accumulated as part of the routine program of the 61-in astrometric reflector. The author is indebted to Dr. Otto G. Franz for making available certain results concerning 01 Orionis prior to publication.

REFERENCES AMBARTSUMIAN, V. AMBARTSUMIAI~, V. AMBARTSUMIAN, V. BAADE, W. a n d MINKOWSK[, R. . BLAAD-W, A. JOHNSON, H. L. a n d BORGM~n% J . PARENAGO, P. P.

1954 1955 1958 1937 1961 1963 1953

Comm. Byurakan Obs., No. 15. Observatory, 75, 72. Rev. Mod. Phys., 30, 944. Ap. J., 8b, 123. B.A.N., 15, 265. Ibid., 17, 115. A.J., U.S.S.R., 30, 249.

132

SA~DAGE, A. R.

SHARPLESS, S. SHARPLESS, S. S]KARPLESS, S.

Ste|lar Systems of the Trapezium Type 1958

Stellar Populations, ed. D. J. K. O'Connell (Amster.

1952 1954 1962

dam: North-Holland Pub. Co.; New Interscience Publishers), p. 149. Ap. J., 116, 251. Ibid., 119, 334. Ibid., 136, 767.

York;